a(n) = Stirling2(n,2)^2 + Stirling2(n,3).

Terms

a(0) =0a(1) =1a(2) =10a(3) =55a(4) =250a(5) =1051a(6) =4270a(7) =17095a(8) =68050a(9) =270451a(10) =1075030a(11) =4276735a(12) =17030650a(13) =67881451a(14) =270777790a(15) =1080817975a(16) =4316294050a(17) =17244046051a(18) =68912400550a(19) =275457464815